Answer:
The absolute number of a number a is written as
|a|
And represents the distance between a and 0 on a number line.
An absolute value equation is an equation that contains an absolute value expression. The equation
|x|=a
Has two solutions x = a and x = -a because both numbers are at the distance a from 0.
To solve an absolute value equation as
|x+7|=14
You begin by making it into two separate equations and then solving them separately.
x+7=14
x+7−7=14−7
x=7
or
x+7=−14
x+7−7=−14−7
x=−21
An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.
The inequality
|x|<2
Represents the distance between x and 0 that is less than 2
picture42
Whereas the inequality
|x|>2
Represents the distance between x and 0 that is greater than 2
picture43
You can write an absolute value inequality as a compound inequality.
$$\left | x \right |<2\: or
−2<x<2
This holds true for all absolute value inequalities.
|ax+b|<c,wherec>0
=−c<ax+b<c
|ax+b|>c,wherec>0
=ax+b<−corax+b>c
You can replace > above with ≥ and < with ≤.
When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.
Sorry If its not what your looking for but i tried
Constraints can be represented by absolute value equations when dealing with inequalities that involve the distance between a variable and a fixed value. Absolute value equations are commonly used to express constraints in mathematical modeling and optimization problems.
Constraints can be represented by absolute value equations when dealing with inequalities that involve the distance between a variable and a fixed value. Absolute value equations are commonly used to express constraints in mathematical modeling and optimization problems. Here's how you can do it:
Representing Constraints with "less than" or "greater than" inequalities:
Suppose you have a variable "x" and a fixed value "a." If you want to impose a constraint that the absolute value of the difference between "x" and "a" is less than some constant "k," you can write it as:
| x - a | < k
For example, if you want to constrain "x" to be within 3 units from 5, you write:
| x - 5 | < 3
Representing Constraints with "less than or equal to" or "greater than or equal to" inequalities:
If you want to impose a constraint that the absolute value of the difference between "x" and "a" is less than or equal to some constant "k," you can write it as:
| x - a | ≤ k
For example, if you want to constrain "x" to be within 2 units from 8, you write:
| x - 8 | ≤ 2
Using absolute value equations allows you to handle situations where the variable needs to be close to a certain value or within a specific range, regardless of whether it is greater or smaller than that value. This flexibility is particularly useful in various mathematical and optimization problems, including linear programming and constrained optimization.
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471.9 is 65% of what amount
471.9=65% × x
671.9/65 = x
x= 10.336923077
Check! Proof!
10.336923077×65%
=671.9
Answers
10.336923077
write a division equation to represent the repeated subtraction 32 take away 8 is 24 24 take away 8 is16 16 take away 8 is 8/8 take away 8 is 0
The repeated subtraction of 8 from 32 until reaching 0 can be represented by the division equation 32 ÷ 8 = 4, showing the number of times 8 is subtracted from 32.
Explanation:The student is performing repeated subtraction of the same number, which can also be represented by a division equation. The repeated subtraction mentioned:
32 take away 8 is 2424 take away 8 is 1616 take away 8 is 88 take away 8 is 0Shows that 32 is being subtracted by 8 until it reaches 0, and this process happens four times. Thus, we can convert this series of subtractions into a division equation: 32 ÷ 8 = 4. This equation means that you can subtract 8 from 32 four times before reaching zero, which is equivalent to dividing 32 by 8.
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How do mathematical graphs help us better understand our world
Answer:
because they help us better analyze data
Step-by-step explanation:
we can see a lot of data on one small thing such as a graph, so we can easily graph data from many years on one graph
Graphs in mathematics help us visually represent equations and display data, allowing us to understand patterns, trends, and relationships between variables.
Explanation:Graphs are an important tool in mathematics as they help us better understand our world by visually representing equations and displaying data. Graphs can show the relationship between different variables, such as in a line graph where one variable is plotted on the horizontal axis and another on the vertical axis. They can also represent data using bar graphs or pie graphs, which help us compare and interpret numerical information.
For example, if we want to analyze the temperature changes throughout a year, we can plot the temperature on the vertical axis and the months on the horizontal axis. By connecting the data points, we can see patterns and trends, such as variations in temperature during different seasons.
In addition, graphs allow us to make predictions and draw conclusions based on the data presented. By analyzing the shape and slope of a graph, we can determine the rate of change, identify maximum and minimum values, and make predictions about future outcomes.
Find the surface area of the right square pyramid. Round your answer to the nearest hundredth. A 117.66 yd^2 B. 123.21 yd^2 C. 145.75 yd^2 D. 182.04 yd ^2
Answer: OPTION C
Step-by-step explanation:
Use the following formula:
[tex]SA=\frac{pl}{2}+B[/tex]
Where p is the perimeter of the base, l is the slant height and B is the area of the base.
The perimeter is:
[tex]p=4*s=4*5.3yd=21.2yd[/tex]
Where s is the side lenght
The slant height is given:
[tex]l=11.1yd[/tex]
The area of the base is:
[tex]B=s^2=(5.3yd)^2=28.09yd^2[/tex]
Where s is the side lenght
Substitute values. Then, the result is:
[tex]SA=\frac{(21.2yd)(11.1yd)}{2}+28.09yd^2)=145.75yd^2[/tex]
Answer:
The correct answer option is C. 145.75 yd^2.
Step-by-step explanation:
We are given a diagram of a right square pyramid with a slant height 11.1 yd, and base edge length 5.3 yd.
We know that the surface area of a right square pyramid is given by:
[tex]\frac{PI}{2} +B[/tex]
where P = perimeter of the base, I = slant height and B = base area.
Perimeter of base = [tex]4 \times 5.3[/tex] = 21.2 yd^2
Base Area = [tex]5.3^3[/tex] = 28.09 yd^2
Surface area of right square pyramid = [tex]\frac{21.2 \times 11.1 }{2} + 28.09[/tex] = 145.75 yd^2
Y=f(x) =2x find f(x) when x=1
Answer:
y = 2
Step-by-step explanation:
Plug 1 into x
2(1) = 2
I need help
Por favor
Leon is helping his baby sister Daphne eat her dinner. There are 121212 peas left in Daphne's bowl and 777 peas squished in her hair
Answer:
Step-by-step explanation:
12:7 I'm pretty sure thats right and if its not then try 7:12
What is the solution
Answer:
Step-by-step explanation:
find all the zeros and write a linear factorization of g(x)=x^4-8x^3+27x^2-50x+50 given that 1+2i is a zero
Answer:
g(x)= (x-(1+2i)) * (x-(1-2i)) * (x-(3-i)) * (x-(3+i))
Please see attached image
Step-by-step explanation:
We can easily solve this equation by using a technical solver or a programming language such as Octave.
The linear factorization of the equation can be obtained directly by finding the zeros of g(x)
Please see attached images for the answer to your problem
g(x)= (x-(1+2i)) * (x-(1-2i)) * (x-(3-i)) * (x-(3+i))
What is the lowest value of the range of the function shown on the graph! Please help asap
The lowest value of the range of the function based on the given coordinates is -2.
To determine the lowest value of the range of the function based on the given coordinates, we need to identify the minimum y-value among the points. The y-values are the second coordinates in each pair.
The given coordinates are:
[tex]\[(-4,5), (0,1), (1,0), (3,-2), (4,-1), (5,0)\][/tex]
The minimum y-value is -2, which corresponds to the point (3, -2). Therefore, the lowest value of the range of the function is -2.
Among the provided options, -2 is the correct answer. The other options (negative infinity, 0, 3) are not supported by the given data. The function attains its lowest value at the point (3, -2), and no lower value is evident from the provided coordinates.
In summary, the lowest value of the range of the function based on the given coordinates is -2.
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Which of the following ordered pairs lies on the graph of h(x)=-3x^2?
A. (1,-4)
B. (1,-2)
C. (1,4)
given, y= -2x^2;
so, when x=1, y= -2((1)^2)= -2
so pair which lie on graph is (x,y) is (1,-2)
Answer:
None
Step-by-step explanation:
We are given that a graph[tex] h(x)=-3x^2[/tex]
We have to find that which pair lie on the given graph.
In order to find the value of ordered pair which lies on the given graph by substituting the value of x=1
If we get h(x)=-4 or -2 or 4 corresponding to x=1 then that pair will be answer.
Substitute x=1 then we get
[tex]h(x)=-3(1)^2=-3[/tex]
The order pair is (1,-3).
Given options do not match with order pair (1,-3).
Hence, answer is none of the above.
Which situation is best modeled by the equation 9+=16 9 + x = 16 ?
Answer:
D.) You pay $9 for a burger and some amount for dessert for a total of $16.
Bottom Right
The directed line segment from L to N has endpoints L(–6, 2) and N(5, –3). What are the x- and y-coordinates of point M, which partitions the directed line segment into the ratio 2:5?
x =
y =
ANSWER
[tex]x = \frac{ - 20}{7}[/tex]
[tex]y=\frac{ 4}{7}[/tex]
EXPLANATION
The x and y coordinates of the point that partition
[tex](x_1,y_1)[/tex]
and
[tex](x_2,y_2)[/tex]
in the ratio m:n is given by:
[tex]x = \frac{mx_{2} + nx_{1}}{m + n} [/tex]
and
[tex]y= \frac{my_{2} + ny_{1}}{m + n} [/tex]
The directed line segment from L to N has endpoints L(–6, 2) and N(5, –3).
We substitute the given points,
[tex]x_1=-6[/tex]
[tex]y_1=2[/tex]
[tex]x_2=5[/tex]
[tex]y_2=-3[/tex]
[tex]m = 2[/tex]
[tex]n = 5[/tex]
This implies that;
[tex]x = \frac{2(5)+ 5( - 6)}{2 + 5} [/tex]
[tex]x = \frac{10 - 30}{2 + 5} [/tex]
[tex]x = \frac{ - 20}{7} [/tex]
[tex]y = \frac{2( - 3)+ 5( 2)}{2 + 5} [/tex]
[tex]y = \frac{ - 6+ 10}{2 + 5} [/tex]
[tex]y=\frac{ 4}{7}[/tex]
Answer:
x = \frac{ - 20}{7}
y=\frac{ 4}{7}
Step-by-step explanation:
What is the measure of ∠W, rounded to the nearest degree?
19°
32°
56°
71°
71°
Step-by-step explanation:This is an isosceles triangle because it has two sides with lengths, hence the angles opposite the equal sides are also equal, that is ∠U = ∠V.
So we can say that:
∠U = ∠V = α
∠W = β
Since the internal angles of a triangle add up to 180 degrees, then:
α + α + β = 180
2α + β = 180
β = 180 - 2α
Using the law of sine:
[tex]\frac{35}{sin\beta} =\frac{30}{sin\alpha} \\ \\ \frac{35}{sin(180 - 2\alpha)} =\frac{30}{sin\alpha} \\ \\ \\ From \ Properties: \\ \\ sin(180-2\alpha)=sin(180)cos2\alpha-sin2\alpha cos(180) \\ \\ = -sin2\alpha(-1)=sin2\alpha \\ \\ Also: \\ \\ sin2\alpha=2sin\alpha cos\alpha[/tex]
Therefore:
[tex]\frac{35}{2sin\alpha cos\alpha} =\frac{30}{sin\alpha} \\ \\ \therefore \frac{35}{60}=cos\alpha \\ \\ \alpha=cos^{-1}(\frac{7}{12})=54.31^{\circ}[/tex]
But we want to know ∠W = β, therefore:
[tex]\beta = 180 - 2\alpha \\ \\ \beta =180-2(54.31)=71.37^{\circ}[/tex]
And rounded to the nearest degree:
∠W = 71°
Find a•b. a=<2,4>, b= <2,5>
Answer:
a • b = 24Step-by-step explanation:
[tex]<a,\ b>\circ<c,\ d>=ac+bd\\\\a=<2,\ 4>,\ b=<2,\ 5>\\\\a\circ b=<2,\ 4>\circ<2,\ 5>=(2)(2)+(4)(5)=4+20=24[/tex]
Leo deposited $2494.05 in an account that earned 2.5% interest compounded weekly for 13 years. After 13 years, how much had Leo earned in interest?
Leo earned approximately $992.08 in interest after 13 years.
Explanation:Compound interest is calculated using the formula:
A = P(1 + r/n)^(nt)
Where:
A = Total future amountP = Principal amountr = Annual interest rate (as a decimal)n = Number of times the interest is compounded per yeart = Number of yearsIn this case, Leo deposited $2494.05 with an interest rate of 2.5% compounded weekly for 13 years. Plugging the values into the formula:
A = 2494.05(1 + 0.025/52)^(52*13)
A = 2494.05(1.00048077)^(676)
A ≈ $3486.13
To find the interest earned, subtract the principal amount from the total future amount:
Interest = A - P
Interest ≈ $3486.13 - $2494.05
Interest ≈ $992.08
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What is the sine equation?
MAX POINTS AND BRAINLIEST !!
Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.
please dont just copy from something you found online cause i'll report u :l
Answer:
x^2+2x+2
Step-by-step explanation:
(x+1)(x+1) or (x+1)^2
x = -1
Answer:
Step-by-step explanation:
x²+8x+15 is the quadratic equation and it can be solved by factoring. By factoring the answer will be (x+3) (x+5) and if it is expanded, the answer will be x²+8x+15. First, you should factorize the equation. Then, find the two numbers that if they are added together the sum will 8 and if they are multiplied the product is 15.
Hope this helps!
Solve the problem below.
57°
123°
114°
66°
Answer:
66
Step-by-step explanation:
George has a box of chocolates. There are 12 pieces of chocolate with nuts and 20 pieces of chocolate without nuts in the box. What is the ratio of pieces of chocolate without nuts to pieces of chocolate with nuts?
A.
15:1
B.
1:15
C.
3:5
D.
5:3
Answer:
Step-by-step explanation:
Good evening ,
________________
the ratio of pieces of chocolate without nuts to pieces of chocolate with nuts:
20:12 = (20:4) : (12:4) = 5:3.
Then the correct answer is D.
____________________________
:)
To find the ratio of chocolates without nuts to chocolates with nuts, divide the quantities of each. With 20 chocolates without nuts and 12 with nuts, the simplified ratio is 5:3, corresponding to answer D.
The question asks us to find the ratio of pieces of chocolate without nuts to pieces of chocolate with nuts. George has 12 pieces of chocolate with nuts and 20 pieces of chocolate without nuts.
To determine the ratio, we divide the number of chocolates without nuts by the number of chocolates with nuts:
Ratio = Number of chocolates without nuts / Number of chocolates with nutsRatio = 20 / 12Ratio = 5 / 3 (after simplifying)Therefore, the correct answer is D. 5:3. This is the ratio of pieces of chocolate without nuts to pieces of chocolate with nuts.
What is 4x4x8 in volume
Answer:
128
Step-by-step explanation:
Do the multiplication:
4 * 4 * 8 = 128
9(6-2v)=-12(v-11) What is the value of v
answer: v = -13
step by step explanation:
Answer:
v = - 13
Step-by-step explanation:
Distribute parenthesis on both sides of the equation
54 - 18v = - 12v + 132 ( add 12v to both sides )
54 - 6v = 132 ( subtract 54 from both sides )
- 6v = 78 ( divide both sides by - 6 )
v = - 13
if jenkins had 254 to spend,then bought 9 t-shirts and had 29 remaining,how much was each shirt? assuming that each shirt costs the same
Answer:
each shirt costs $25
Step-by-step explanation:
we can make an equation using x as the cost of each shirt. since 254 was the total, they will=254 together , and since we have 9 shirts, its 9x. we can use this info to create the equation 9x+29=254. we subtract 29 on each side to get 9x=225. we then divide 9 on both sides to get x=25. so each shirt costs $25
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In 2005, there were 12,300 students at college A, with a projected enrollment increase of 500 students per year. In the same year there were 18,550 students at college B with a projected enrollment decline of 750 students per year. According to these projections, when will the colleges have the same enrollment? What will the enrollment in each college at that time?
Answer: 5 years
14,800 students enrolled
Step-by-step explanation:
Let x represent the number of years and
Let y represent the number of students enrolled
College A: y = 12,300 + 500x
College B: y = 18,550 - 750x
Use substitution Method to solve:
12,300 + 500x = 18,550 - 750x
+750x +750x
12,300 + 1250x = 18,550
-12,300 -12,300
1250x = 6250
x = 5
Input x = 5 into one of the equations to solve for y.
y = 12,300 + 500x
= 12,300 + 500(5)
= 12,300 + 2500
= 14,800
I need help please???
Answer:
x < 8
Step-by-step explanation:
Given
x + 4 < 12
Isolate x on the left side by subtracting 4 from both sides
x < 8 ← is the solution
Answer:
x< 8
Step-by-step explanation:
x+4<12
x+4<12
-4 -4
x<8
30000 equals how many ones
The number 30,000 is made up of 30,000 individual ones. This basic mathematical concept helps understand the scale of numbers and aid in quick approximations. It can be compared to estimating powers of 10 for mental calculations.
Explanation:The question '30000 equals how many ones' can be interpreted as asking how many single units there are in 30,000. This is a basic math concept dealing with place value and integer understanding. Each individual unit is a 'one', and therefore, in 30,000, there are 30,000 of these individual units, each one contributing to the total value of the number. In other words, 30,000 is comprised of 30,000 ones.
To relate this to practical applications, consider the example where the square root of 10 is roughly estimated as 3, because 3³ (which is 3 x 3 x 3) equals 27, which is near to 10² (100), giving us an approximation that is useful for mental calculations. Similarly, the basic concept of powers of 10 can be applied here, with 10³ being 1,000, hence 30 x 10³ being 30,000. So, when you're working with large numbers like 30,000, knowing that it is made up of 30,000 ones can help you understand its scale and make quick approximations in everyday calculations.
The number 8 is a perfect 1. Square and cube 2. Cube 3. Square
Answer:
2. CubeStep-by-step explanation:
[tex]8=2\cdot2\cdot2=2^3\\\\\text{It's a perfect cube}[/tex]
What are the characteristics of trapezoid ?
Answer:
"A trapezoid is a quadrilateral with two parallel sides and, usually, two nonparallel sides."
Step-by-step explanation:
"A trapezoid is a quadrilateral with two parallel sides and, usually, two nonparallel sides. A quadrilateral is a geometric shape that has four sides. Some specialized types of trapezoid are the parallelogram and the isosceles trapezoid.
The two parallel sides of a trapezoid are its bases while the legs are the nonparallel sides. Geometric analysis of a trapezoid includes calculating the height, median and area. The height of a trapezoid is a line segment that runs perpendicular to the bases. The median, or mid-segment, is a line that is parallel to the bases and connects the midpoints of each leg. The area is calculated with a formula using the lengths of each base and the height.
A parallelogram is usually defined as a trapezoid, although it has two pairs of parallel sides instead of just one. An isosceles trapezoid has congruent base angles and equal leg lengths."
A trapezoid is a four-sided polygon with one pair of parallel sides. Its key characteristics include parallel sides, supplementary adjacent angles, and specific area calculation. The median connects the midpoints of the legs, with a length that averages the bases.
A trapezoid is a four-sided polygon, also known as a quadrilateral, with one pair of opposite sides parallel. These parallel sides are known as the bases of the trapezoid, while the other two sides are called the legs.
Key Characteristics:
Parallel Sides: The most defining feature of a trapezoid is that it has exactly one pair of parallel sides.Angle Properties: The angles adjacent to each leg are supplementary, meaning they add up to 180 degrees.Area Calculation: The area of a trapezoid can be calculated using the formula A = 1/2 × (Base1 + Base2) × Height, where Base1 and Base2 are the lengths of the parallel sides, and Height is the perpendicular distance between them.Median: The median (or midsegment) of a trapezoid is a line segment that connects the midpoints of the legs, and its length is the average of the lengths of the bases.These characteristics are essential for identifying and working with trapezoids, especially in various mathematical problems and geometric constructions.
The table shows the number of minutes spent doing different exercises. The mean spent exercising was 18.2 minutes. How many minutes were spent doing sit ups? (URGENT HELP) (ANSWER 4/11/19)
Answer:
15
Step-by-step explanation:
Call the unknown time x.
The mean is the sum of the numbers divided by the number of numbers.
There are 5 numbers.
(8 + 10 + 38 + x + 20)/5 = 18.2
(x + 76)/5 = 18.2
x + 76 = 91
x = 15
Answer:
Step-by-step explanation:
Add all the scores you do know
8 + 10 + 38 + 20 = 76
Now put in an ex for the situps.
76 + x
There are 5 subjects
(76 + x) /5 = 18.2
The average was 18.2
Multiply both sides by 5
5*(76 + x ) / 5 = 18.2 * 5
Cancel the left combine the right.
76 + x = 91
Subtract 76 from both sides
76 - 76 + x = 91 - 76
x = 15
Help me please and thank you
Answer:
The answer to this problem is 32
Step-by-step explanation:
How to get this answer is u divide the base by the area of meters. so 276/12=32. Hope this helps and i hope its right!
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Put it into a calculator. The method is correct. The answer is 23